A mechanic is draining old oil from a vehicle into a waste oil catch pan that has a maximu… — Armed Services Vocational Aptitude Battery (ASVAB)

A mechanic is draining old oil from a vehicle into a waste oil catch pan that has a maximum capacity of $15$ quarts. The catch pan already contains $4\frac{2}{3}$ quarts of oil from a previous job. If the vehicle's engine holds $7\frac{3}{4}$ quarts of oil, and all of it is drained into the catch pan, how much more room, in quarts, is left in the catch pan?

A
$3\frac{5}{12}$
B
$3\frac{2}{7}$
$2\frac{7}{12}$ Answer
D
$7\frac{1}{4}$

Answer

The correct answer is

2\frac{7}{12}

To find the remaining capacity, first add the two amounts of oil using a common denominator of 12 (

4\frac{8}{12} + 7\frac{9}{12} = 11\frac{17}{12} = 12\frac{5}{12}

quarts). Then, subtract this total from the pan's capacity of 15. By borrowing, 15 becomes

14\frac{12}{12}

. Subtracting

12\frac{5}{12}

leaves

2\frac{7}{12}

quarts.

Step-by-Step Solution

Determine the total amount of oil that will be in the catch pan by adding the existing oil and the vehicle's oil.

4\frac{2}{3} + 7\frac{3}{4}

The pan's occupied space is the sum of what was already there and what is being added.

Find a common denominator to add the fractions.

The least common multiple of 3 and 4 is 12. Convert the fractions:

4\frac{8}{12} + 7\frac{9}{12}

Fractions must have the same denominator before they can be added.

Add the whole numbers and the numerators, then simplify.

4 + 7 = 11

and

\frac{8}{12} + \frac{9}{12} = \frac{17}{12}

. Since

\frac{17}{12} = 1\frac{5}{12}

, the total is

11 + 1\frac{5}{12} = 12\frac{5}{12}

quarts.

Combines the mixed numbers to find the total volume of oil.

Subtract the total volume of oil from the catch pan's maximum capacity.

15 - 12\frac{5}{12}

The remaining room is the difference between the total capacity and the occupied space.

Borrow 1 from the whole number 15 to perform the subtraction.

Rewrite

15

14\frac{12}{12}

. Subtract:

14\frac{12}{12} - 12\frac{5}{12} = (14 - 12) + (\frac{12}{12} - \frac{5}{12}) = 2\frac{7}{12}

quarts.

Borrowing allows subtraction of the fractional part.

Key Concept

Adding mixed numbers with unlike denominators and subtracting mixed numbers from whole numbers by borrowing.

Question

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Step-by-Step Solution

Key Concept

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